Question

A charged particle goes undeflected in a region containing electric and magnetic fields. It is possible that

$\left(i\right)\overrightarrow{E}||\overrightarrow{B},\overrightarrow{V}||\overrightarrow{E}$
$\left(ii\right)\overrightarrow{E}$ is perpendicular to $\overrightarrow{B}$
and both are perpendicular to $\overrightarrow{V}$
$\left(iii\right)\overrightarrow{V}||\overrightarrow{B}$, but $\overrightarrow{E}$ is not parallel to $\overrightarrow{B}$
$\left(iv\right)\overrightarrow{E}||\overrightarrow{B}$, but $\overrightarrow{V}$ is not parallel to $\overrightarrow{E}$.

• A. Only $\left(i\right)$ and $\left(ii\right)$ are true
• B. Only $\left(ii\right)$ and $\left(iii\right)$ are true
• C. Only $\left(iii\right)$ and $\left(iv\right)$ are true
• D. Only $\left(i\right),\left(ii\right)$ and $\left(iii\right)$ are true

Answer 1

The correct option is A Only $\left(i\right)$ and $\left(ii\right)$ are true

As we know that,

$\overrightarrow{F_m}=q(\overrightarrow{V}\times \overrightarrow{B})$ and $\overrightarrow{F_e}=q\overrightarrow{E}$

In $\left(i\right)$ and $\left(ii\right)$, it will traverse undeflected and the path will be straight line.
But in $\left(ii\right)$ and $\left(iv\right)$ it will traverse in a deviated path (curved or helical path).